Find the radius of gyration of a plate covering the region bounded by y=x.x=6, and the x-axis with respect to the x-axis. The radius of gyration is (Type an exact answer.)
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The given problem involves finding the radius of gyration of a plate covering a specific region with respect to the x-axis. The radius of gyration is a measure of how far the mass of an object is distributed from its axis of rotation, and it is defined as the square root of the ratio of the moment of inertia to the mass of the object. The moment of inertia is a measure of an object's resistance to rotational motion and is defined as the integral of the square of the distance from each point in the object to the axis of rotation, multiplied by the density of the object. In this problem, we are given a specific plate covering the region bounded by y = x, x = 6, and the x-axis, and we are asked to find its radius of gyration with respect to the x-axis. To do this, we need to first find the moment of inertia of the plate with respect to the x-axis, which involves integrating the product of the density of the plate and the square of the distance from each point in the plate to the x-axis. By applying the appropriate formula and solving for the radius of gyration, we can obtain an exact answer. The concept of moment of inertia and radius of gyration are important tools in physics and engineering and have many applications in the analysis of systems and structures.
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The radius of gyration of the plate covering the given region with respect to the x-axis is 6 units.
The radius of gyration of a plate covering the region bounded by y=x, x=6, and the x-axis with respect to the x-axis can be found using the formula:
Radius of Gyration (K) = √(I/A),
where I is the second moment of area (also called the moment of inertia) with respect to the x-axis, and A is the area of the region.
First, we need to find the area of the triangle formed by the region bounded by y=x, x=6, and the x-axis. The area of the triangle is:
A = (1/2) * base * height = (1/2) * 6 * 6 = 18 square units.
Next, we need to find the second moment of area (I) with respect to the x-axis. For a triangle with base 'b' and height 'h', the moment of inertia about the x-axis is given by:
I = (1/12) * b * h^3 = (1/12) * 6 * (6^3) = 648 cubic units.
Now, we can find the radius of gyration (K) using the formula:
K = √(I/A) = √(648/18) = √(36) = 6 units.
So, the radius of gyration of the plate covering the given region with respect to the x-axis is 6 units.
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Related Questions
(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.
Answers
Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm
Perimeter of a polygonPerimeter = 150 cmPerimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)
150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4
150 = 6x + 24
150 - 24 = 6x
126 = 6x
x = 126/6
x = 21
The longest side of the polygon is (x + 8)
= 21 + 8
= 29 cm
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A farmer has asked you for advice on the best strategy for planting wheat and corn on her 500-acre farm. To make it through harvest time, each acre of wheat she plants will require 1 person-day of labor and other expenses of $20. Each acre of corn she plants will require 5 person-days of labor and expenses of $30. The farmer has $11,400 and 1480 person-days of labor available, and she expects to make a profit of $90 per acre of wheat and $120 per acre of corn. If x = acres of wheat and y = acres of corn, which of the following is NOT a constraint?
x + y ≤ 500
20x + 30y ≤ 11,400
y ≥ 5x + 30
x + 5y ≤ 1480
Answers
The constraint that is NOT valid is " \(y > = 5x + 30\) "
To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.
To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.
The constraints are as follows:
\(x + y < = 500\) : This constraint ensures that the total planted area does not exceed the farm size.\(20x + 30y < = 11,400\) : This constraint represents the budget limitation.\(y > = 5x + 30\) : This constraint is NOT valid because it suggests that the number of acres of corn must be greater than or equal to 5 times the number of acres of wheat plus 30. However, there is no information provided to support this relationship.\(x + 5y < = 1480\) : This constraint limits the total available person-days of labor.By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.
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To estimate the mean number of text messages sent by cell-phone users, a researcher chooses a location on a college campus in the city and surveys the first 50 people who walk past. These subjects are asked how many text messages they have sent in the past 24 hours. Is it likely that bias will be present in the sample?
A) Because this is a convenience sample, it is likely that the sample results will be unbiased.
B) Because this is a convenience sample of college students, it is likely that bias is present and that the results will overestimate the mean number of text messages sent.
C) Because this is a convenience sample of college students, it is likely that bias is present and that the results will underestimate the mean number of text messages sent.
D) Because this is a voluntary response sample of college students, it is likely that bias is present and that the results will overestimate the mean number of text messages sent.
Answers
Answer:
WARNING! C IS INCORRECT 2021.
MOST LIKELY (B): Because this is a convenience sample of college students, it is likely that bias is present and that the results will overestimate the mean number of text messages sent.
ED2021
please help is this correct
Answers
Answer:
yes its correct
Step-by-step explanation:
you dont really need work because its really just substitution.
Is inches allowed to be used in science when measuring?
Answers
HURRY WILL GIVE BRANILIST!
Answers
Answer:
Hope this helps :)
Step-by-step explanation:
I believe it is the second one because it is the only one that makes a rectangular prism with with thin sides and a wide rectangular base.
A cyclist rides down a long straight road at a velocity (in m/min) given by v(t)=100−10t, for 0 st ≤10. a. How far does the cyclist travel in the first 3 min ? b. How far does the cyclist travel in the first 5 min ? c. How far has the cyclist traveled when her velocity is 55 m/min ? a. The cyclist travels m in the first 3 min. b. The cyclist travels m in the first 5 min. c. When the cyclist's velocity is 55 m/min, she has traveled (Round to two decimal places as needed.)
Answers
a. The cyclist travels 127.5 meters in the first 3 minutes. b. The cyclist travels 187.5 meters in the first 5 minutes. c. When the cyclist's velocity is 55 m/min, she has traveled 187.5 meters.
a. To find how far the cyclist travels in the first 3 minutes, we need to calculate the definite integral of the velocity function v(t) from t = 0 to t = 3:
∫[0,3] (100 - 10t) dt
Using the power rule of integration, we have:
\(= [100t - 5t^2/2]\) evaluated from t = 0 to t = 3
\(= [100(3) - 5(3)^2/2] - [100(0) - 5(0)^2/2]\)
= [300 - 45/2] - [0]
= 255/2
= 127.5 m
b. Similarly, to find how far the cyclist travels in the first 5 minutes, we integrate the velocity function from t = 0 to t = 5:
∫[0,5] (100 - 10t) dt
\(= [100t - 5t^2/2]\) evaluated from t = 0 to t = 5
\(= [100(5) - 5(5)^2/2] - [100(0) - 5(0)^2/2]\)
= [500 - 125/2] - [0]
= 375/2
= 187.5 m
c. We need to find the time t when the velocity v(t) is equal to 55 m/min. Setting v(t) = 55 and solving for t:
100 - 10t = 55
10t = 100 - 55
10t = 45
t = 4.5 min
To determine the distance traveled at this time, we can use the result from part (b). The cyclist travels 187.5 meters in the first 5 minutes. Since 4.5 minutes is less than 5 minutes, the distance traveled when the velocity is 55 m/min is also 187.5 meters.
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I need help fast plss
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The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°
Finding the measures of the anglesFrom the question, we have the following parameters that can be used in our computation:
The transversal lines and the other lines
So, we have
∠1 = 180 - 53
Evaluate
∠1 = 127°
Also, we have
∠5 = 53°
By vertical angles, we have
∠2 = 53°
∠3 = 127°
Next, we have
∠4 = 127 - 90°
∠4 = 37°
Solving further, we have
∠6 = 90°
By corresponding angles, we have
∠7 = 37°
∠9 = 180 - 90 - 53°
∠9 = 37°
∠10 = 90 + 53°
∠10 = 143°
∠8 = 143°
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can someone answer this pls
its iready math.
Answers
Answer:
4 x 4 x 10
Step-by-step explanation:
A = 8 x 4 x 5 = 160
1) 8 x 4 x 6 = 192
2) 6 x 10 x 2 = 120
3) 5 x 4 x 7 = 140
4) 4 x 4 x 10 = 160
Answer:
Option 4, Length 4ft, Width 4ft, Height 10ft
Step-by-step explanation:
Prism A and B have the same volume. Volume is found by multiplying length, width and height together.
The volume of prism A is
8 x 4 x 5 = 160 cubic ft
Multiply all the 4 options together until you get a match of 160 cubic ft
8 x 4 x 6 = 192 cubic ft
6 x 10 x 2 = 120 cubic ft
5 x 4 x 7 = 140 cubic ft
4 x 4 x 10 = 160 cubic ft
Factor each polynomial
Answers
Answer: x^2 (x+1) (4x-9)
Step-by-step explanation:
We can test the equation above x^2 (x+1) (4x-9) to see if it is true or not by rewriting it
x^2 ( 4x^2 -9x +4x -9)
x^2 (4x^2 - 5x -9)
4x^4 - 5x^3 - 9x^2
So x^2 (x+1) (4x-9) is the correct answer for this equation!
If you can please give me a Brainliest, I only need one more to become an Expert, thank you
Find the intervals on which f is increasing and the intervals on which it is decreasing.
f(x) = x^ 3 − x ^2 − 2x
Answers
The function f(x) = x^3 - x^2 - 2x is increasing on the intervals (-∞, (1 - √7) / 3) and ((1 + √7) / 3, +∞), and it is decreasing on the interval ((1 - √7) / 3, (1 + √7) / 3).
First, let's find the derivative of f(x):
f'(x) = 3x^2 - 2x - 2
To determine the intervals of increasing and decreasing, we need to find the critical points by setting f'(x) = 0 and solving for x:
3x^2 - 2x - 2 = 0
Using the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4(3)(-2))) / (2(3))
x = (2 ± √(4 + 24)) / 6
x = (2 ± √28) / 6
x = (2 ± 2√7) / 6
x = (1 ± √7) / 3
The critical points are x = (1 + √7) / 3 and x = (1 - √7) / 3.
Now, we can analyze the intervals:
Increasing intervals:
From (-∞, (1 - √7) / 3)
From ((1 + √7) / 3, +∞)
Decreasing intervals:
From ((1 - √7) / 3, (1 + √7) / 3)
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Please answer correctly !!!! Will mark Brianliest !!!!!!!!!!!!!!
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A multiple linear regression model is to be constructed to determine if there is a relationship between a dependent variable (y) and two independent variables (x1 and x2). A random sample of size n has been collected and the values of x1i, x2i and yi for i = 1, 2, ..., n have been recorded. The residuals (ei) in this analysis are defined as the difference between the observed values of y and the values of y predicted by the regression equation.Select the condition that is one of the assumptions of a valid multiple linear regression model:the relationship between the dependent and independent variables is linearthe residuals are constantthe independent variables are independent of the dependent variablethe relationship between the dependent and independent variables is quadratic
Answers
The condition that is one of the assumptions of a valid multiple linear regression model is: the relationship between the dependent and independent variables is linear.
Condition that is one of the assumptions of a valid multiple linear regression model is that the relationship between the dependent and independent variables is linear. This means that the change in the dependent variable is proportional to the change in each independent variable, and there is no curved or nonlinear relationship between them. The assumption of linear independence of the independent variables is also important, meaning that they are not highly correlated with each other.
The assumption of constant residuals means that the errors in the model are consistent across all values of the independent variables. The assumption of a quadratic relationship between the dependent and independent variables is not appropriate for a multiple linear regression model.
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A racetrack is in the shape of an ellipse 100 feet long and 50 feet wide. What is the width 10 feet from a vertex?
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A racetrack is in the shape of an ellipse 100 feet long and 50 feet wide the width of the racetrack 10 feet away from a vertex is 16 feet (twice the absolute value of ±8).
To find the width 10 feet from a vertex of the ellipse-shaped racetrack, first, identify the coordinates of the vertices.
The center of the ellipse is at (0,0), and the semi-major axis is 50 feet (half the length of the ellipse), while the semi-minor axis is 25 feet (half the width of the ellipse).
Therefore, the vertices are located at (0,±50). We can see that 10 feet away from one of the vertices, the x-coordinate will still be close to 0, while the y-coordinate will be close to ±40.To find the width at this point, we can use the equation of the ellipse, which is given by (x^2/50^2) + (y^2/25^2) = 1
Plugging in x = 0 and y = ±40, we get:
(0^2/50^2) + (±40^2/25^2) = 1
Simplifying, we get:
±(40/5) = ±8
Therefore, the width of the racetrack 10 feet away from a vertex is 16 feet (twice the absolute value of ±8).
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Please help me w this!!!
Answers
Answer:
Step-by-step explanation:
X =90
Is (4,4) a solution of the graphed system of inequalities? Choose 1 answer: Yes No
Answers
Answer:
The answer is No
I literally tried Yes
Is this relation a function? {(3, 2), (5, 9), (11, 25)}
Answers
Answer:
Yes
Step-by-step explanation:
None of the X values are the same number.
I will mark as brainliest if answer
Answers
Answer:
D
I believe the second one is none of the above
Step-by-step explanation:
61-27
Answer:
34 degrees.
Step-by-step explanation:
m<AOC - m<BOC = <AOB = 61 - 27 = 34
for the second one i think it's none.
Which could be the measures of the three angles of an acute triangle?
Answers
As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.
An acute triangle is a triangle that has three acute angles, which are angles that measure less than 90 degrees. All three angles of an acute triangle must be acute, so they must measure less than 90 degrees. The measures of the three angles of an acute triangle can be any combination of angles that add up to less than 180 degrees.
Here are some examples of the measures of the three angles of an acute triangle:
45 degrees, 45 degrees, 90 degrees
30 degrees, 60 degrees, 90 degrees
35 degrees, 40 degrees, 105 degrees
60 degrees, 60 degrees, 60 degrees (this would be an acute equilateral triangle)
As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.
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Besides being simple for its own sake, what other advantage do simple models usually have?
a) Higher accuracy
b) Greater complexity
c) Easier interpretation
d) More detailed predictions
Answers
The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.
This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.
Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.
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Is a dilation with a scale factor greater than 1 is a reduction?
Answers
When the scale factor is greater than one, then the dilation is not a reduction.
What is a dilation?
Dilation is a process of changing a thing. It is a process of transformation that to make the objects smaller or larger, with the use of specific scale factor.
The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.
What is a center of dilation?
Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.
Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.
Figure size increased, when the scale factor is greater than 1.
Thus, the dilation will be a expansion, when the scale factor is a greater than one.
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b. Write an exponential equation for the following situation. The drug dosage is 500 mg. The drug is
eliminated at a rate of 5.2% per hour. Use D = the amount of the drug in milligrams and t = time in
hours.
What is the equation for this?
Answers
Answer:
D(t) = 500(0.948)^tStep-by-step explanation:
Initial amount = 500 mg
Elimination rate = 5.2% = 0.052 times per hour
This is the exponential decay and the equation would be:
D(t) = 500*(1 - 0.052)^t ⇒ D(t) = 500(0.948)^tGeneral equation
y=ab^xWhere
a is initial amount
b is rate of change
Here b=1-0.052=0.948
So equation
D=500(0.948)^t-x -y when x= -12 and y=2
Answers
Hello! My name is Chris and I’ll be helping you with this problem.
Date: 9/28/20 Time: 11:32
Answer:
-14
Explanation:
-12 - 2 = -14
I hope this helped answer your question! Have a great rest of your day!
Furthermore,
Chris
Which number is a rational number? OA √15 OB. 2.6457513110... O c. 17.156 OD. 3√85
Answers
Answer:
"O c. 17.156"
Step-by-step explanation:
A is not a rational number because it cannot be written as a fraction [with two integers] or an integer (the square root of 15 is equal too 3.87298334...)
B is not a rational number because it also goes on forever, just like A.
C is a rational number because it does not go on forever.
D is like A and B, it goes on forever.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
The balance after the grace period is $25,000. A payment of $5,000 is made on the 10th day. A payment of $5,000 is made on the 20th day. What is the average daily balance?
Answers
The average daily balance after 20 days is; $1750
Average BalanceThe initial balance after grace period is; $25,000
Afterwards, A payment of $5,000 each is made on the 10th and 20th day.
Hence, the total balance after 20 days is;
= $25,000 + $5000 + $5000= $35,000.The average daily balance is therefore the quotient of $35,000 and 20 days
The average daily balance = $35,000/20Average daily balance = $1750Read more on average;
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2. draw the lewis dot structure for each of the following molecules or ions. determine the number of bonding and nonbonding electron domains and indicate their electron domain and molecular geometries BF2
Answers
The Lewis dot structure for BF2 is:
F B F
\ /
B
/ \
F B F
In this molecule, there are three atoms (one boron and two fluorine) and a total of 12 valence electrons. Boron is in group 3, so it has 3 valence electrons, while each fluorine atom has 7 valence electrons.
To form the Lewis dot structure, we first place the atoms in a linear arrangement. Each fluorine atom shares one electron with the boron atom, giving a total of two shared electrons (or one bond) between the boron and each fluorine atom. This gives us a total of four electrons (or two bonds) between the boron and the two fluorine atoms.
The remaining four electrons are placed as nonbonding electron pairs around each fluorine atom to satisfy the octet rule. Therefore, there are a total of two bonding domains and two nonbonding electron domains around the boron atom. The electron domain geometry is tetrahedral, and the molecular geometry is linear.
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y = x^2 - 4x + 4
Find the discriminant.
Determine the number
of real solutions.
Answers
Answer:
The discriminant is 0
There is 1 real solution
Step-by-step explanation:
Use the discriminant formula, D = b² - 4ac
In the equation y = x² - 4x + 4, a is 1, b is -4, and c is 4.
Plug in these values into the formula:
D = b² - 4ac
D = (-4)² - 4(1)(4)
D = 16 - 4(4)
D = 16 - 16
D = 0
So, the discriminant is 0.
With a discriminant of zero, there is one real solution.
So, the number of real solutions is 1.
Help Math help help help ASAP
Answers
Answer:
Step-by-step explanation:
a) 2,35 x 10^9
b) 2,5 x 10^7
c) 9 x 10^4
b=2.5x10^7
c=D
which is an equation with a degree of 3, a zero located at x=4 and a y-intercept located at (0,60)
Answers
The degree 3 polynomial equation is 1/2(4 - x)(x - 1)(x - 2).
What is a polynomial equation?A polynomial equation is one in which a polynomial is set to zero. It is an equation composed of variables, non-negative integer exponents, and coefficients, as well as operations and an equal sign. It has various exponents. The highest one represents the equation's degree.A third-degree polynomial is defined as p(x) = ax³ + bx² + cx + d, where 'a' is not equal to zero. Because it has a degree of three, it is also known as a cubic polynomial.Here given,
With zeros and a coefficient, the function is:
f(x) = a(x - 4)(x - 1)(x - 2)
Regarding the y-intercept:
f(0) = a(0 - 4)(0 - 1)(0 - 2)
4 = a(-4)(-1)(-2)
4 = -8a
a = -1/2
As a result, the function is:
f(x) = -1/2(x - 4) (x - 1)(x - 2)
= 1/2(4 - x)(x - 1)(x - 2)
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If a family has five girls and plans to have another child, answer the following if the probability of the event of a boy being born is \( \frac{1}{2} \), and births are independent events. a. What is
Answers
In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.
The previous births do not affect the probability of the next birth since each birth is an independent event.
The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.
Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.
In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.
Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.
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